With a CRT monitor you will generally just have a blank screen when the signal is lost, some display a message.
TFT's will display "No signal" if the signal is lost or goes out of range. I think you can rule out a faulty cable as you have used two different cables so far. [One with each monitor].
The first thing to look at is the graphic card. Is it fully slotted home? Turn off your PC's power and also at the wall socket as modern motherboards still have a trickle feed to them even though turned off.
Remove the side panel of your case and press firmly but don't use too much force on the graphic card to make sure it is full seated, check the screw at the case end of the card slot to make sure it's tight and holding the card in place. If it's not then when you push the monitor cable in you may be moving the card slightly.
Try the above and please post back to let us know how you get on before looking at other settings. j.